a) $\sqrt{5x + 12}$ có nghĩa
$\Leftrightarrow 5x + 12 \geq 0$
$\Leftrightarrow 5x \geq - 12$
$\Leftrightarrow x \geq - \dfrac{12}{5}$
b) $\sqrt{\dfrac{-4}{3 - 2x}}$ có nghĩa
$\Leftrightarrow \dfrac{-4}{3 - 2x} \geq 0$
$\Leftrightarrow 3 - 2x < 0$
$\Leftrightarrow 2x > 3$
$\Leftrightarrow x > \dfrac{3}{2}$
c) $\sqrt{\dfrac{x+5}{3-x}}$ có nghĩa
$\Leftrightarrow \dfrac{x+5}{3 - x} \geq 0$
$\Leftrightarrow \left[\begin{array}{l}\begin{cases}x + 5 \geq 0\\3 - x > 0\end{cases}\\\begin{cases}x + 5 \leq 0\\3 - x< 0\end{cases}\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}\begin{cases}x \geq -5\\x < 3\end{cases}\\\begin{cases}x\leq - 5\\x > 3\end{cases}\end{array}\right.$
$\Leftrightarrow - 5 \leq x < 3$
d) $\sqrt{x - 3} - \sqrt{2x + 1}$ có nghĩa
$\Leftrightarrow \begin{cases}x - 3 \geq 0\\2x + 1 \geq 0\end{cases}$
$\Leftrightarrow \begin{cases}x \geq 3\\x \geq - \dfrac{1}{2}\end{cases}$
$\Leftrightarrow x \geq 3$
